Effect of errors in the migration velocity model of PS-converted waves on traveltime accuracy in prestack Kirchhoff time migration in weak anisotropic media

Abstract

We investigated the effect of errors in the migration-velocity model of PS-converted waves on the traveltime calculated in prestack Kirchhoff time migration in weak anisotropic media. The prestack-Kirchhoff-time-migration operator contains four parameters: the PS-converted-wave velocity, the vertical velocity ratio, the effective velocity ratio, and the anisotropic parameter. We derived four error factors that correspond to those parameters. Theoretical and numerical analyses of the error factors show them all to be inversely proportional to the velocity and to traveltime. Traveltime errors for shallow events usually are larger than for deep events. Error in PS-converted-wave velocity causes the largest traveltime error, and error in the vertical velocity ratio causes the smallest traveltime error. For a small horizontal-distance/depth ratio, the error in the effective velocity ratio affects traveltime more than does the anisotropic-parameter error. However, the anisotropic-parameter error affects traveltime more when the horizontal-distance/depth ratio is larger. Traveltime errors caused by errors in effective velocity ratio and the anisotropic parameter mainly stem from the converted-S-wave raypath of the PS-converted waves. To save processing time and cost, PS-wave velocity can be estimated accurately without an accurate vertical velocity ratio, effective velocity ratio, and anisotropic parameter. These findings are useful for understanding PS-wave behavior and for PS-wave imaging in anisotropic media.